From “Uh Oh!” to “Aha!”

Over 20 years ago, just out of college, I applied for a job at TERC after seeing an ad in a newspaper. A project called Investigations in Number, Data, and Space was looking for a classroom observer. I had spent most of my college years volunteering in an elementary classroom once a week, so I sent a writing sample – from a course I’d taken with Ted Sizer – and got an interview. The last step? Meet Susan Jo Russell, the Principal Investigator of the project.

We chatted and she asked me about my experience with math. I said I’d always done pretty well in math and, in an effort to be positive, I added:

Me: I always liked how tidy it was, how you get an answer you can put a box around.

Then she asked me to solve a story problem. A division problem. In my head.

Me [in my head]: Uh oh!

I had always been good at math. I was a good memorizer. I excelled in following the steps and getting the right answer. Doing the division algorithm in my head was not easy, especially on the spot. I managed by writing furiously on what Marilyn Burns would call my “mental chalkboard”. Looking back, I didn’t have another way to think about the problem, nor a sense that there were other ways.

When Susan Jo talked about writing a curriculum that would help students solve problems in ways that made sense to them, I didn’t know what that might mean. But it intrigued me. It made me think about:

• Elementary school friends who were not good at memorizing, at blindly following a series of steps. And who were therefore seen as — and who saw themselves as — not good at math. (I remember publicly pretending that I didn’t understand subtraction with regrouping in 2nd grade because no one else did.)

• A high school friend who I could see understood things, like why the steps worked. I would ask, “But how do you know that??” He could not explain, and I could not fathom, how he knew these things that we hadn’t been taught.

What I came to understand was that a curriculum like Investigations could empower my elementary school friends to expect math to make sense and to expect that they could make sense of it.

It could also make explicit the kinds of ideas and thinking that my high school friend “could just see,” for everyone. Discovering that an equation I might have seen in algebra could be used to describe an actual situation, that it could be represented with objects and seen and described in different ways, was one of many “aha!”s I have had over the years.

My hope is that a curriculum like Investigations provides students with many such moments. And fewer adults saying, “But why didn’t I ever know that?”

Megan has been involved in the development and writing of all three editions of Investigations in Number, Data, and Space. Originally a classroom observer who spent many hours in field test classrooms, she is now a senior author, specializing in grades K-2. She has also developed and facilitated professional development around Investigations in particular and elementary mathematics in general.

4 Comments

Eileen Goodspeed
on September 30, 2017 at 11:43 pm

Students today are so lucky! When faced with a problem like Susan Jo’s, they won’t be caught off guard. Having been taught in a classroom that emphasizes the Math Practices, they will be able to make sense of the problem, use their reasoning to solve it, and communicate their thinking. I have long admired Investigations integration of the Math Practices, long before they were called that.

How are teachers responding to the spotlight on the MP’s in the new edition?

Interesting you should ask that Eileen! It’s a question we are hoping to learn more about as people implement the 3rd edition. We are certainly hearing good things about the ways the new features make the Math Practices explicit and highlight good opportunities to focus on specific practices. (Check out some of the comments on Karen’s blog post (https://investigations.terc.edu/its-not-whats-new-its-whats-old/) We hope that Inv3 can help people envision what these practices might look like in the elementary grades — e.g. what does it mean for a 5-year-old to “look for and make use of structure”?

I am noticing that the teachers I work with are beginning to see explicit connections between the content of an Investigation and the focus math practices. They are commenting on how the MP notes in the sidebars actually leverage the content work.